Did anyone else notice that? During a rain storm (Haven't tried any other weather yet) I accdiently fell in the river near the bridge, and it brought me to the other side. It was certainly odd XD
If you jump in, there's only one spot that you can resurface at each part of the river. So the river carries you for a way until you reach that spot. Drowning myself is one of my favorite GB activities.
Besides, you can get various items when you fall in the water.
At the beginning at the game, I have a lot of stamina so I often jump to the water to get some interesting goods (such as sea urchin, and coins). They have good prices